Question

Решить уравнение x^2∙(x – 2)^2– 3∙(x – 1)^2–1= 0

Answer 1

(x²-2x)²-3(x²-2x+1)-1.
x⁴-4x³+4x²-3x²+6x-3-1=0.
x⁴-x³-3x³+3x²-2x²+2x+4x-4=0.
x³(x-1)-3x²(x-1)-2x(x-1)+4(x-1)=0.
(x-1)(x³-3x²-2x+4)=0.
(x-1)(x³-x²-2x²+2x-4x+4)=0.
(x-1)(x²(x-1)-2x(x-1)-4(x-1))=0.
(x-1)(x-1)(x²-2x-4)=0.
(x-1)²=0. x=1.
x1,2=(2±√(4+16))/2=1±√5.